Both of my neighbors on either side run natural gas, so I assume the lines are close by. My house is all electric and the heating bills are nuts in the winter. I want to look into the cost of putting in a small natural gas furnace and hot water heater. It's a tiny house (around 1,000 sq ft on one level) so I'm thinking I can get by pretty cheap on a furnace (maybe even just a gas powered "wood stove" set in the living room, but the plumbing to run the gas line might be killer. Any guesses as to what it could cost?

I had to get me meter upgraded last year. To pull a new, larger, pipe and install a new meter was $800 IIRC.
That was for a pretty big meter though, so I would imagine, if you don't need that, it would be cheaper.